Creating an edge between two vertexes
Make smart use of modifiers here. You have a repeating shape, use an Array modifier instead of modelling it all one by one by hand.

For the face keep it simple. Just use the Poke Faces Alt + P operator on a simple unsubdivided face.

Move the resulting vertex down to vertically align with the bottom vertex of the face, then move it forward to make the protruding "pyramid" shape.